Sharp conditions for scattering and blow-up for a system of NLS arising in optical materials with χ3 nonlinear response

DOI10.1080/03605302.2021.1925916zbMath1479.35761arXiv2011.13769OpenAlexW3108305256MaRDI QIDQ5012786

Van Duong Dinh, Alex H. Ardila, Luigi Forcella

Publication date: 25 November 2021

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.13769

zbMATH Keywords

scatteringblow-upnonlinear Schrödinger systemsMorawetz estimatescubic-type interactions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Scattering theory for PDEs (35P25) Diffraction, scattering (78A45) NLS equations (nonlinear Schrödinger equations) (35Q55) Lasers, masers, optical bistability, nonlinear optics (78A60) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Blow-up in context of PDEs (35B44) Methods of ordinary differential equations applied to PDEs (35A24) Time-dependent Schrödinger equations and Dirac equations (35Q41) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (8)

On finite time blow-up for a 3D Davey-Stewartson system ⋮ Ground state energy threshold and blow-up for NLS with competing nonlinearities ⋮ Stable standing waves for a Schrödinger system with nonlinearχ3 response ⋮ On the stability of solitary waves in the NLS system of the third-harmonic generation ⋮ Some results for a system of NLS arising in optical materials with χ³ nonlinear response ⋮ Blow-up results for systems of nonlinear Schrödinger equations with quadratic interaction ⋮ Long Time Dynamics of Nonradial Solutions to Inhomogeneous Nonlinear Schrödinger Equations ⋮ Scattering for quadratic-type Schrödinger systems in dimension five without mass-resonance

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